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Welcome to our Math lesson on Another Property of Exponents Used in Algebraic Expressions, this is the seventh lesson of our suite of math lessons covering the topic of The Meaning of Expressions. Simplifying Expressions, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Another Property of Exponents Used in Algebraic Expressions
One of the most outstanding properties of exponents is the one that says: "If any term of an algebraic expression is raised at a certain power, all its elements are raised at that power. If any variable of that term is already raised in a certain power, the exponents multiply with each other."
In symbols, we have
(axm yn )k = ak xm ∙ k ∙ yn ∙ k
For example,
(2xy2 )3 = 23 x3 y2 ∙ 3
= 8x3 y6
Now, let's see all the properties discussed in this tutorial applied in a single exercise.
Example 4
Express the following algebraic expression in the simplest terms.
3pq3 + (12p2 q)2 - 5p4 q2 - 2p2 ∙ 3p2 q2 + 2pq3
Solution 4
3pq3 + (12p2 q)2 - 5p4 q2 - 2p2 ∙ 3p2 q2 + 2pq3
= 3pq3 + 122 (p2 )2 q2 - 5p4 q2 - 2p2 ∙ 3p2 q2 + 2pq3
= 3pq3 + 144p4 q2 - 5p4 q2 - 2p2 ∙ 3p2 q2 + 2pq3
= 3pq3 + 144p2 + 2 q2 - 5p4 q2 - (2 ∙ 3) p2 + 2 q2 + 2pq3
= 3pq3 + 144p4 q2 - 5p4 q2 - 6p4 q2 + 2pq3
= 144p4 q2 - 5p4 q2 - 6p4 q2 + 3pq3 + 2pq3
= (144 - 5 - 6) p4 q2 + (3 + 2)pq3
= 133p4 q2 + 5pq3
To ease the classification of like terms, we can underline them with the same kind of line or write them using the same colour, as we will see in the following example. This is done only after finishing with power, multiplications and divisions.
Example 5
Express the following algebraic expression in the simplest terms.
2x - 3x ∙ 4y + 5xy - (2x2 )6 - 7x2 + 60x12-5xy
= 2x - 3x ∙ 4y + 5xy - 26 ∙ (x2 )6-7x2 + 60x12 - 5xy
= 2x - 3x ∙ 4y + 5xy - 128x12 - 7x2 + 60x12 - 5xy
= 2x - 12xy + 5xy - 128x12 - 7x2 + 60x12 - 5xy
= -75x12 + 2x - 12xy
More The Meaning of Expressions. Simplifying Expressions Lessons and Learning Resources
Expressions Learning Material| Tutorial ID | Math Tutorial Title | Tutorial | Video
Tutorial | Revision
Notes | Revision
Questions |
|---|
| 6.1 | The Meaning of Expressions. Simplifying Expressions | | | | |
| Lesson ID | Math Lesson Title | Lesson | Video
Lesson |
|---|
| 6.1.1 | What are (Algebraic) Expressions | | |
| 6.1.2 | Calculating the Value of an Algebraic Expression | | |
| 6.1.3 | Terms of Algebraic Expressions | | |
| 6.1.4 | Simplifying Algebraic Expressions | | |
| 6.1.5 | Ordering the Terms of Algebraic Expressions | | |
| 6.1.6 | Multiplying and Dividing Terms of an Algebraic Expression | | |
| 6.1.7 | Another Property of Exponents Used in Algebraic Expressions | | |
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